

A031688


Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 100.


3



2501, 123953, 203482, 204385, 206197, 304825, 425273, 568741, 726193, 727898, 734738, 906665, 1119805, 1124041, 1334554, 1341493, 1346129, 1565626, 1568129, 1570634, 1573141, 1578161, 1580674, 1583189, 1590746, 1593269, 1828633, 2126605, 2138285, 2144137
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OFFSET

1,1


LINKS



MATHEMATICA

cf100Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; OddQ[len] && cf[[(len+1)/2]] == 100]; Select[Range[2200000], cf100Q] (* Harvey P. Dale, May 29 2016 *)


PROG

(Python)
from sympy import continued_fraction_periodic
A031688_list = [n for n, s in ((i, continued_fraction_periodic(0, 1, i)[1]) for i in range(1, 10**5)) if isinstance(s, list) and len(s) % 2 and s[(len(s)1)//2] == 100] # Chai Wah Wu, Jun 11 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Definition corrected and terms corrected and extended by Harvey P. Dale, May 29 2016


STATUS

approved



